The figures are not drawn to scale. Figure 1 shows a rectangular piece of paper EGHK that measures 22 cm by 15 cm. EF = JH = 4 cm. The paper is folded along the dotted line FJ such that point G touches point K, as shown in Figure 2.
- Find the area of Figure 2. EFJHK, after the folding.
- In Figure 2, ∠EFK is 74°. Find ∠FJH in Figure 2.
(a)
Area of Rectangle EGHK
= 22 x 15
= 330
Area of Triangle EFK
=
12 x 4 x 15
= 30 cm
2 Area of Triangle FKJ
= (330 - 30 - 30) ÷ 2
= 270 ÷ 2
= 135 cm
2 Area of EFJHK
= 135 + 30 + 30
= 195 cm
2 (b)
∠KFJ
= (180° - 74°) ÷ 2
= 106 ÷ 2
= 53° (Angles on a straight line)
∠FJH
= 360° - 90° - 90° - 53°
= 127° (Sum of angles in a quadrilateral)
Answer(s): (a) 195 cm
2; (b) 127°